Finite Group Databasebeta

← C151×#18730 #50323655

Subgroups — C151×#18730 #50323655

Order 38656.

864 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3550×C151C211yesmaximal, characteristic
2#3230×C151C211yesmaximal, characteristic, complemented
3#3227×C151C211yesmaximal, characteristic
4#3139×C151C211yesmaximal, characteristic, complemented
5#1638×C151C214yesmaximal, complemented
6#1637×C151C214yesmaximal, complemented
7#1544×C151C211yesmaximal, characteristic, complemented
8#1485×C151C211yesmaximal, characteristic, complemented
9#1484×C151C211yesmaximal, characteristic
10#563×C151—22no—
11#559×C151—21no—
12Q82×C151—21no—
13#556×C151—21no—
14#556×C151C2212yes—
15D4×Q8×C151—21no—
16D4×Q8×C151C2212yes—
17#542×C151—22no—
18#542×C151—22no—
19#536×C151—22no—
20#533×C151C2211yescharacteristic
21#533×C151C2211yescharacteristic
22#532×C151C2211yescharacteristic
23C2×C4⋊Q8×C151C2211yescharacteristic
24#500×C151—21no—
25#498×C151—21no—
26#491×C151—22no—
27#487×C151—21no—
28#487×C151C2212yes—
29#487×C151C2212yes—
30#486×C151—21no—
31#484×C151—22no—
32#481×C151—22no—
33#477×C151C2214yes—
34#476×C151C2214yes—
35#431×C151C2211yescharacteristic
36#431×C151C2211yescharacteristic
37#419×C151—22no—
38C4×M16×C151C2211yescharacteristic
39#332×C151C2212yes—
40#332×C151C2212yes—
41Q8⋊C8×C151C2214yes—
42D4⋊C8×C151C2214yes—
43C2×#41×C151—21no—
44C22×Q8×C151—22no—
45C22×Q8×C151—21no—
46C2×M16×C151—21no—
47C4⋊Q8×C151—24no—
48C4⋊Q8×C151—22no—
49C4⋊Q8×C151—22no—
50C4⋊Q8×C151—21no—
51C4⋊Q8×C151—21no—
52C4⋊Q8×C151—21no—
53C4⋊Q8×C151D411yescharacteristic
54C4⋊Q8×C151D411yescharacteristic
55C4⋊Q8×C151D411yescharacteristic
56C4⋊Q8×C151C2312yes—
57C4⋊Q8×C151C2311yescharacteristic
58C4⋊Q8×C151C2311yescharacteristic
59#127×C151D411yescharacteristic
60#126×C151—24no—
61#126×C151—24no—
62#125×C151—21no—
63#125×C151D412yes—
64#124×C151—24no—
65#124×C151—22no—
66#124×C151—22no—
67#124×C151—21no—
68#123×C151—24no—
69#123×C151—24no—
70C22⋊Q8×C151—24no—
71C22⋊Q8×C151—21no—
72C22⋊Q8×C151—21no—
73C22⋊Q8×C151—21no—
74C22⋊Q8×C151—22no—
75C22⋊Q8×C151—24no—
76C22⋊Q8×C151—22no—
77C22⋊Q8×C151D412yes—
78#121×C151—21no—
79#121×C151D412yes—
80C4×Q8×C151—22no—
81C4×Q8×C151—22no—
82C4×Q8×C151—21no—
83C4×Q8×C151—21no—
84C4×Q8×C151—21no—
85C4×Q8×C151C2312yes—
86C4×D4×C151—22no—
87C4×D4×C151—22no—
88C4×D4×C151—21no—
89C4×D4×C151C2312yes—
90#117×C151—21no—
91#117×C151—22no—
92#117×C151D412yes—
93C2×C4⋊C4×C151—21no—
94C2×C4⋊C4×C151—21no—
95C2×C42×C151C2311yescharacteristic
96#107×C151—24no—
97#106×C151—24no—
98C4⋊C8×C151C2312yes—
99C4⋊C8×C151C2312yes—
100#103×C151—24no—
101#103×C151—24no—
102#103×C151—24no—
103#102×C151—24no—
104C22⋊C8×C151—21no—
105C22⋊C8×C151—21no—
106#97×C151—21no—
107C4×C8×C151—21no—
108C4×C8×C151—21no—
109C4×C8×C151C2312yes—
110#41×C151—82no—
111C2×Q8×C151—24no—
112C2×Q8×C151—21no—
113C2×Q8×C151—21no—
114C2×Q8×C151—21no—
115C2×Q8×C151—21no—
116C2×Q8×C151—22no—
117C2×Q8×C151—44no—
118C2×Q8×C151—41no—
119C2×Q8×C151—84no—
120C2×Q8×C151C2×D412yes—
121C2×D4×C151—22no—
122C2×D4×C151—21no—
123C2×D4×C151—21no—
124C2×D4×C151C2×D412yes—
125C22×C4×C151—24no—
126C22×C4×C151—22no—
127C22×C4×C151—41no—
128C22×C4×C151C2×D411yescharacteristic
129C22×C4×C151C2×D411yescharacteristic
130C22×C4×C151C2×D411yescharacteristic
131M16×C151—42no—
132C2×C8×C151—22no—
133C2×C8×C151—22no—
134C2×C8×C151—22no—
135C4⋊C4×C151—24no—
136C4⋊C4×C151—24no—
137C4⋊C4×C151—21no—
138C4⋊C4×C151—21no—
139C4⋊C4×C151—21no—
140C4⋊C4×C151—21no—
141C4⋊C4×C151—22no—
142C4⋊C4×C151—22no—
143C4⋊C4×C151—22no—
144C4⋊C4×C151—21no—
145C4⋊C4×C151—21no—
146C4⋊C4×C151—22no—
147C4⋊C4×C151—22no—
148C4⋊C4×C151—22no—
149C4⋊C4×C151—41no—
150C4⋊C4×C151—41no—
151C4⋊C4×C151C2×D412yes—
152C4⋊C4×C151C2×D412yes—
153C4⋊C4×C151C2×D412yes—
154C4⋊C4×C151C2×D412yes—
155C22⋊C4×C151—24no—
156C22⋊C4×C151—24no—
157C22⋊C4×C151—24no—
158C22⋊C4×C151—22no—
159C22⋊C4×C151—22no—
160C22⋊C4×C151—22no—
161C22⋊C4×C151—22no—
162C42×C151—24no—
163C42×C151—22no—
164C42×C151—22no—
165C42×C151C2×D411yescharacteristic
166C42×C151C2×D411yescharacteristic
167C42×C151C2×D411yescharacteristic
168C42×C151C2411yescharacteristic
169C23×C151—22no—
170C23×C151#12011yescharacteristic
171Q8×C151—24no—
172Q8×C151—44no—
173Q8×C151—42no—
174Q8×C151—42no—
175Q8×C151—42no—
176Q8×C151—81no—
177Q8×C151—84no—
178Q8×C151—82no—
179D4×C151—24no—
180D4×C151—42no—
181D4×C151—81no—
182D4×C151—82no—
183C2×C4×C151—22no—
184C2×C4×C151—22no—
185C2×C4×C151—22no—
186C2×C4×C151—22no—
187C2×C4×C151—22no—
188C2×C4×C151—22no—
189C2×C4×C151—22no—
190C2×C4×C151—22no—
191C2×C4×C151—44no—
192C2×C4×C151—42no—
193C2×C4×C151—84no—
194C2×C4×C151—82no—
195C2×C4×C151#12011yescharacteristic
196C2×C4×C151#12011yescharacteristic
197C2×C4×C151#12011yescharacteristic
198C2×C4×C151C22×D411yescharacteristic
199C2×C4×C151C22×D411yescharacteristic
200C2×C4×C151C22×D411yescharacteristic
201C8×C151—42no—
202C8×C151—42no—
203C8×C151—42no—
204C22×C151—21no—
205C22×C151—21no—
206C22×C151—21no—
207C22×C151—42no—
208C22×C151—42no—
209C22×C151—42no—
210C22×C151C2×#12011yescharacteristic
211C4×C151—21no—
212C4×C151—21no—
213C4×C151—21no—
214C4×C151—42no—
215C4×C151—42no—
216C4×C151—42no—
217C4×C151—42no—
218C4×C151—42no—
219C4×C151—82no—
220C4×C151#45412yes—
221C4×C151#57712yes—
222C4×C151#57812yes—
223C2×C151—41no—
224C2×C151—82no—
225C2×C151#300911yescharacteristic
226C2×C151#301111yescharacteristic
227C2×C151C2×#45411yescharacteristic
228#18730C15111yesmaximal, characteristic, direct product factor, Sylow
229C151#1873011yescharacteristic, direct product factor, Sylow
230#3550C2×C15111yescharacteristic
231#3230C2×C15111yescharacteristic, complemented
232#3227C2×C15111yescharacteristic
233#3139C2×C15111yescharacteristic, complemented
234#1638C2×C15114yescomplemented
235#1637C2×C15114yescomplemented
236#1544C2×C15111yescharacteristic, complemented
237#1485C2×C15111yescharacteristic, complemented
238#1484C2×C15111yescharacteristic
239#563—22no—
240#559—21no—
241Q82—21no—
242#556—21no—
243#556C22×C15112yes—
244D4×Q8—21no—
245D4×Q8C22×C15112yes—
246#542—22no—
247#542—22no—
248#536—22no—
249#533C22×C15111yescharacteristic
250#533C22×C15111yescharacteristic
251#532C22×C15111yescharacteristic
252C2×C4⋊Q8C22×C15111yescharacteristic
253#500—21no—
254#498—21no—
255#491—22no—
256#487—21no—
257#487C22×C15112yes—
258#487C22×C15112yes—
259#486—21no—
260#484—22no—
261#481—22no—
262#477C22×C15114yes—
263#476C22×C15114yes—
264#431C22×C15111yescharacteristic
265#431C22×C15111yescharacteristic
266#419—22no—
267C4×M16C22×C15111yescharacteristic
268#332C22×C15112yes—
269#332C22×C15112yes—
270Q8⋊C8C22×C15114yes—
271D4⋊C8C22×C15114yes—
272C2×#41—21no—
273C22×Q8—22no—
274C22×Q8—21no—
275C2×M16—21no—
276C4⋊Q8—24no—
277C4⋊Q8—22no—
278C4⋊Q8—22no—
279C4⋊Q8—21no—
280C4⋊Q8—21no—
281C4⋊Q8—21no—
282C4⋊Q8D4×C15111yescharacteristic
283C4⋊Q8D4×C15111yescharacteristic
284C4⋊Q8D4×C15111yescharacteristic
285C4⋊Q8C23×C15112yes—
286C4⋊Q8C23×C15111yescharacteristic
287C4⋊Q8C23×C15111yescharacteristic
288#127D4×C15111yescharacteristic
289#126—24no—
290#126—24no—
291#125—21no—
292#125D4×C15112yes—
293#124—24no—
294#124—22no—
295#124—22no—
296#124—21no—
297#123—24no—
298#123—24no—
299C22⋊Q8—24no—
300C22⋊Q8—22no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—22no—
305C22⋊Q8—24no—
306C22⋊Q8D4×C15112yes—
307#121—21no—
308#121D4×C15112yes—
309C4×Q8—22no—
310C4×Q8—22no—
311C4×Q8—21no—
312C4×Q8—21no—
313C4×Q8—21no—
314C4×Q8C23×C15112yes—
315C4×D4—22no—
316C4×D4—22no—
317C4×D4—21no—
318C4×D4C23×C15112yes—
319#117—21no—
320#117—22no—
321#117D4×C15112yes—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C42C23×C15111yescharacteristic
325#107—24no—
326#106—24no—
327C4⋊C8C23×C15112yes—
328C4⋊C8C23×C15112yes—
329#103—24no—
330#103—24no—
331#103—24no—
332#102—24no—
333C22⋊C8—21no—
334C22⋊C8—21no—
335#97—21no—
336C4×C8—21no—
337C4×C8—21no—
338C4×C8C23×C15112yes—
339#41—82no—
340C2×Q8—24no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8—21no—
344C2×Q8—21no—
345C2×Q8—22no—
346C2×Q8—44no—
347C2×Q8—41no—
348C2×Q8—84no—
349C2×Q8C2×D4×C15112yes—
350C2×D4—22no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4C2×D4×C15112yes—
354C22×C4—24no—
355C22×C4—22no—
356C22×C4—41no—
357C22×C4C2×D4×C15111yescharacteristic
358C22×C4C2×D4×C15111yescharacteristic
359C22×C4C2×D4×C15111yescharacteristic
360M16—42no—
361C2×C8—22no—
362C2×C8—22no—
363C2×C8—22no—
364C4⋊C4—24no—
365C4⋊C4—24no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4C2×D4×C15112yes—
381C4⋊C4C2×D4×C15112yes—
382C4⋊C4C2×D4×C15112yes—
383C4⋊C4C2×D4×C15112yes—
384C22⋊C4—24no—
385C22⋊C4—24no—
386C22⋊C4—24no—
387C22⋊C4—22no—
388C22⋊C4—22no—
389C22⋊C4—22no—
390C22⋊C4—22no—
391C42—24no—
392C42—22no—
393C42—22no—
394C42C2×D4×C15111yescharacteristic
395C42C2×D4×C15111yescharacteristic
396C42C2×D4×C15111yescharacteristic
397C42C24×C15111yescharacteristic
398C23—22no—
399C23#120×C15111yescharacteristic
400Q8—24no—
401Q8—44no—
402Q8—42no—
403Q8—42no—
404Q8—42no—
405Q8—81no—
406Q8—84no—
407Q8—82no—
408D4—24no—
409D4—42no—
410D4—81no—
411D4—82no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—44no—
421C2×C4—42no—
422C2×C4—84no—
423C2×C4—82no—
424C2×C4#120×C15111yescharacteristic
425C2×C4#120×C15111yescharacteristic
426C2×C4#120×C15111yescharacteristic
427C2×C4C22×D4×C15111yescharacteristic
428C2×C4C22×D4×C15111yescharacteristic
429C2×C4C22×D4×C15111yescharacteristic
430C8—42no—
431C8—42no—
432C8—42no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—42no—
437C22—42no—
438C22—42no—
439C22C2×#120×C15111yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—42no—
444C4—42no—
445C4—42no—
446C4—42no—
447C4—42no—
448C4—82no—
449C4#454×C15112yes—
450C4#577×C15112yes—
451C4#578×C15112yes—
452C2—41no—
453C2—82no—
454C2#3009×C15111yescharacteristic
455C2#3011×C15111yescharacteristic
456C2C2×#454×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#532×C151C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #3230×C151C2semidirect
4. #3139×C151C2semidirect
5. #1638×C151C2semidirect
6. #1637×C151C2semidirect
7. #1544×C151C2semidirect
8. #1485×C151C2semidirect
228. #18730C151direct (N × H)
229. C151#18730direct (N × H)
231. #3230C2×C151semidirect
233. #3139C2×C151semidirect
234. #1638C2×C151semidirect
235. #1637C2×C151semidirect
236. #1544C2×C151semidirect
237. #1485C2×C151semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#3550×C1512
#3230×C1512
#3227×C1512
#3139×C1512
#1638×C1512
#1637×C1512
#1544×C1512
#1485×C1512
#1484×C1512
#18730151